What are the differences in scope between statistical AI and classical AI?
Statistical AI, arising from machine learning, tends to be more concerned with "inductive" thought: given a set of patterns, induce the trend. 
Classical AI is the branch of artificial intelligence research that concerns itself with attempting to explicitly represent human knowledge in a declarative form i.e given a set of constraints, deduce a conclusion.
 Another difference is that C++ tends to be a favorite language for statistical AI while LISP dominates in classical AI.

A system can't be more intelligent without displaying properties of both inductive and deductive thought. This lends many to believe that in the end, there will be some kind of synthesis of statistical and classical AI.